When you're selling a product at a loss, holding production back to increase demand for it due to rareness while you can take the time to reduce the loss you make on it makes a measure of sense.
You claim that people are not more likely to buy a rare product than a common product, but this is not true; it creates a "gotta have it" atmosphere and high eBay prices, so every one that people see on the shelf will sell because someone will snatch it and sell it on eBay.
That's true and it does make some sense...but not in a market where you need to get a foothold...as much of the product in the hands of consumers as possible.
Rareness mainly stimulates purchases from speculators, who really only compromise a microfraction of the market. And speculators also cater to hardcore gamers. Once all of the hardcore gamers have their systems, they have nobody else to sell to. They would then have to keep pricing the product lower and lower until the margin they get on the sale doesn't sufficiently cover the cost and time required to originally acquire the product. Grandma and Uncle Joe are not going to pay $50 more, over retail, to buy a Wii or go out of their way to find one. Nor is any other average consumer. Any hardcore gamer, who really wanted a Wii by now, would have already gotten one. By limiting supply, you kill off sales from the average consumer. And it's the average consumers that you really want to buy the product.
Having a hot, rare product only increases the speed at which it sells, not the quantity of units that sell. If you want a Wii and see one on a store shelf (knowing that Wii's are almost always sold out everywhere) you will be more inclined to impulsively purchase it on the spot. However, if Wii's were easy to find, you might instead feel secure waiting a month or more to buy the Wii. But you were going to buy the Wii, anyway...only you're doing it now rather than at some point later. If you never wanted a Wii, you are not suddenly going to buy one just because it's rare and one is sitting right in front of you.
It doesn't matter how high the demand is on your product....if you don't actually have the product to sell, you're not going to make any money. You don't make money on demand, you make money on selling products. Consumers are fickle and demand is not a stable thing. People are only patient for so long. If an average consumer wants something and they can never find it, they will eventually either give up or make an alternate purchase.
My whole point, with all of this, is that it doesn't make any sense (business or otherwise) that Nintendo would purposefully restrict their supply of Wii's. Diverting available supply to another market is a completely different topic. The goal of any business is to have enough products available to match the amount that consumers are willing to buy. To not have enough product available to match demand would mean lost sales (resulting in lower revenues and lost profit). To have more product available than demanded would mean more overhead and other costs (resulting in lower revenues and lost profit). Also, a business wants to sustain or increases sales. Long term, rare products (by their nature) do neither of those things.
